The present invention relates to reject analysis.
One of the major objectives of reject analysis is to ensure that a process is working within or better than the bounds of its historical capability. Constant monitoring of the rejects from a process is the first step to ensure that procedures, especially new ones, are not having an adverse effect on the overall output.
It is well-known to control a process so that it operates within specified boundaries. This can be achieved using statistical process control (SPC) techniques which involve constant monitoring of the process. Such techniques may be univariate wherein a single variable of the process is monitored or multivariate where more than one variable is monitored. Multivariate SPC techniques are particularly well suited to use with complex processes in which a large number of variables are monitored routinely to assess the status of a particular process. Some of the variables may not be independent and the degree to which they are correlated is often unknown, and such processes cannot be assessed adequately with conventional control techniques.
A single parameter known as Hotelling""s T2 (Hotelling, H, (1931), The Generalisation of Student""s Ratio, Ann. Math. Statist., 2, pages 360-378) can be used successfully as an indicator in multivariate SPC techniques to determine the current status of the process. This parameter utilises all the information contained in the monitored variables as well as accounting for any correlation between them. The state of a process is determined by the magnitude of T2, for example, if it exceeds the 95% limit, then the process is behaving in a significantly different way to that of the standard.
The underlying analysis required to deduce the T2 parameter provides a method of quickly identifying causes of process failure. Corrective action guidelines (CAG) can be developed to facilitate the operation of the system and to provide help for common control failure conditions.
Previously known procedures for reject analysis were effectively based on univariate statistical process control (SPC) techniques. However, these techniques are not suitable for use with complex processes where, for each process, a large number of variables are routinely monitored to assess the status of that process. Some of the variables in such a process may not be independent and the degree to which the variables are correlated is often unknown, making it difficult to assess the status of the process.
It is therefore an object of the present invention to implement multivariate statistical process control (SPC) techniques for reject analysis in order to overcome the problems mentioned above.
In accordance with one aspect of the present invention, there is provided a method of carrying out reject analysis on a repetitive process, the method comprising the steps of:
a) defining a set of variables for the process;
b) sampling data relating to rejects obtained from the process for the defined set of variables;
c) defining a model of the process from the sampled data;
d) applying limits to the model indicative of out-of-control conditions;
e) monitoring the process for out-of-control situations; and
f) taking corrective action to bring the process back into control when the applied limits have been exceeded;
characterised in that the model is defined using principal component analysis in terms of parameters T2 and Qres, where T2 is derived from the sum of the squares of the scores of each of the principal components of the model and Qres is derived from a weighted sum of the squares of the scores of the principal components not included in the model.
If the T2 parameter exceeds a predetermined limit, the contribution of the scores to that T2 parameter value is interrogated to determine which score is the primary contributor. The score which forms the primary contributor is interrogated further to assess which of the monitored variables is of significance.
An additional parameter Qres may also be determined for the process. If either of the T2 or Qres parameters exceeds predetermined limits, then it indicates a significant change compared with the reference system.
T2 and Qres monitor different out-of-control behaviour, T2 assessing systematic variability within the model and Qres the systematic non-random variability not captured by the model.
The term xe2x80x98repetitive processxe2x80x99 means a routine process which is repeated according to requirement for that process. For example, processing of X-ray films in a radiology department is a routine process which is repeated as required.
By using multivariate SPC techniques, the sensitivity of detecting out-of-control conditions for reject analysis is increased in comparison with existing manual and labour intensive methods.
In accordance with the present invention, the method of reject analysis described herein provides a key parameter on which to base a quality assurance strategy. As a result, the method is also applicable in other applications, for example, photofinishing.
It also provides a sound statistical foundation on which to formulate any quality improvement strategy, and a simple parameter is derived for used in everyday operations.
A potential benefit of using Hotelling""s T2 parameter is that it additionally yields vital information which can be used to correct any control failure problem with efficacy.
In particular T2 determines, the aim and limits for rejects from a process in terms of monitored variables or classification categories. An immediate assessment of any analysis period relative to a reference position can be determined. Moreover, the method also allows the causes of increased or decreased reject rates to be quickly established and then measures, can be implemented either to correct problems or new algorithms generated to reflect the improved working position.
Furthermore, the use of the method of the present invention ensures that other measured variables or categories found to impact the reject performance characteristics of a process at a later stage can be included as an extension to that method at any time.